Finite Group Databasebeta

← #7647024

Subgroups — #7647024

Order 512.

4112 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42826C212yesmaximal, complemented
2#42824C212yesmaximal, complemented
3#42821C212yesmaximal, complemented
4#42819C212yesmaximal, complemented
5#42185C214yesmaximal, complemented
6#42183C214yesmaximal, complemented
7#39752C212yesmaximal
8#39496C212yesmaximal
9#39179C212yesmaximal
10#38963C212yesmaximal
11#38103C214yesmaximal
12#37877C214yesmaximal
13#37609C212yesmaximal
14#37562C212yesmaximal
15#37197C214yesmaximal, complemented
16#37197C214yesmaximal, complemented
17#35643C212yesmaximal, complemented
18#35642C212yesmaximal, complemented
19#35339C212yesmaximal
20#35304C211yesmaximal, characteristic
21#35235C211yesmaximal, characteristic
22#35221C212yesmaximal, complemented
23#35221C212yesmaximal, complemented
24#35146C212yesmaximal
25#34948C211yesmaximal, characteristic
26#34878C211yesmaximal, characteristic
27#34196C211yesmaximal, characteristic
28#34128C211yesmaximal, characteristic
29C2×#2320C211yesmaximal, characteristic
30C22×C4×Q8C2211yescharacteristic
31#2864C2214yes—
32#2864C2214yes—
33#2863C2214yes—
34#2863C2214yes—
35#2857C2212yes—
36#2855C2214yes—
37#2851C2212yes—
38#2845C2214yes—
39#2844C2214yes—
40#2843C2214yes—
41#2843C2214yes—
42#2809C2214yes—
43#2809C2214yes—
44#2806C2214yes—
45#2806C2214yes—
46#2806C2214yes—
47#2806C2214yes—
48#2805C2214yes—
49#2805C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2799C2214yes—
55#2799C2214yes—
56#2799C2214yes—
57#2799C2214yes—
58#2792C2214yes—
59#2792C2214yes—
60#2792C2214yes—
61#2792C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2791C2214yes—
65#2791C2214yes—
66#2774C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2755C2214yes—
71#2755C2214yes—
72#2755C2214yes—
73#2755C2214yes—
74#2666C2214yes—
75#2666C2214yes—
76#2666C2214yes—
77#2666C2214yes—
78#2666C2214yes—
79#2666C2214yes—
80#2666C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2666C2214yes—
84#2666C2214yes—
85#2660C2212yes—
86#2659C2214yes—
87#2647C2214yes—
88#2647C2214yes—
89#2647C2212yes—
90#2646C2214yes—
91#2627C2214yes—
92#2627C2214yes—
93#2612C2214yes—
94#2612C2214yes—
95#2612C2212yes—
96#2612C2212yes—
97#2612C2214yes—
98#2606C2214yes—
99#2606C2214yes—
100#2606C2212yes—
101#2606C2214yes—
102#2606C2212yes—
103#2606C2212yes—
104#2605C2214yes—
105#2605C2214yes—
106#2605C2212yes—
107#2605C2214yes—
108#2605C2212yes—
109#2605C2212yes—
110#2590C2214yes—
111#2590C2214yes—
112#2590C2214yes—
113#2588C2214yes—
114#2588C2214yes—
115#2588C2214yes—
116#2586C2214yes—
117#2586C2214yes—
118#2586C2214yes—
119#2585C2214yes—
120#2585C2214yes—
121#2585C2214yes—
122#2584C2212yes—
123#2584C2212yes—
124#2584C2212yes—
125#2582C2212yes—
126#2581C2212yes—
127#2581C2212yes—
128#2581C2212yes—
129#2571C2212yes—
130#2570C2214yes—
131#2570C2214yes—
132#2570C2214yes—
133#2570C2214yes—
134#2570C2212yes—
135#2570C2214yes—
136#2569C2211yescharacteristic
137#2569C2214yes—
138#2569C2214yes—
139#2569C2212yes—
140#2569C2212yes—
141#2569C2212yes—
142#2569C2211yescharacteristic
143#2569C2214yes—
144#2569C2212yes—
145#2568C2212yes—
146#2567C2212yes—
147#2565C2212yes—
148#2565C2212yes—
149#2565C2212yes—
150#2552C2212yes—
151#2552C2212yes—
152#2550C2212yes—
153#2550C2212yes—
154#2550C2212yes—
155#2550C2212yes—
156#2549C2214yes—
157#2549C2211yescharacteristic
158#2549C2211yescharacteristic
159#2549C2212yes—
160#2549C2212yes—
161#2520C2214yes—
162#2520C2214yes—
163#2511C2214yes—
164#2509C2212yes—
165#2509C2212yes—
166#2509C2212yes—
167#2508C2212yes—
168#2508C2212yes—
169#2507C2212yes—
170#2507C2212yes—
171#2507C2214yes—
172#2507C2212yes—
173#2453C2212yes—
174#2453C2212yes—
175#2453C2212yes—
176#2453C2212yes—
177#2453C2212yes—
178#2451C2212yes—
179#2451C2212yes—
180#2451C2212yes—
181#2442C2212yes—
182#2442C2212yes—
183#2442C2212yes—
184#2440C2212yes—
185#2438C2214yes—
186#2438C2214yes—
187#2438C2212yes—
188#2438C2212yes—
189#2438C2214yes—
190#2438C2214yes—
191#2438C2214yes—
192#2402C2212yes—
193#2402C2214yes—
194#2399C2212yes—
195#2356C2212yes—
196#2356C2214yes—
197#2355C2212yes—
198#2355C2214yes—
199#2351C2212yes—
200Q8×C4⋊C4C2212yes—
201#2344C2211yescharacteristic
202#2344C2212yes—
203#2344C2211yescharacteristic
204#2344C2212yes—
205#2344C2212yes—
206#2344C2214yes—
207Q8×C22⋊C4C2211yescharacteristic
208Q8×C22⋊C4C2212yes—
209Q8×C22⋊C4C2211yescharacteristic
210#2331C2212yes—
211#2331C2212yes—
212#2330C2212yes—
213#2330C2212yes—
214#2329C2214yes—
215#2329C2214yes—
216#2320C2212yes—
217#2320C2211yescharacteristic
218#2320C2211yescharacteristic
219#2320C2211yescharacteristic
220#2320C2211yescharacteristic
221#2320C2214yes—
222#2320C2212yes—
223#2320C2212yes—
224#2320C2212yes—
225#2320C2212yes—
226#2320C2212yes—
227#2320C2211yescharacteristic
228#2320C2211yescharacteristic
229#2317C2214yes—
230#2316C2214yes—
231C4×#125C2212yes—
232C4×#125C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2212yes—
235#2296C2212yes—
236#2295C2212yes—
237#2295C2212yes—
238#2295C2212yes—
239#2295C2214yes—
240C2×#391C2212yes—
241C2×#389C2212yes—
242C2×#387C2214yes—
243#2285C2212yes—
244#2285C2211yescharacteristic
245#2285C2212yes—
246#2283C2211yescharacteristic
247#2283C2212yes—
248#2283C2211yescharacteristic
249#2283C2212yes—
250C2×#383C2212yes—
251C2×#382C2212yes—
252#2276C2211yescharacteristic
253#2276C2211yescharacteristic
254C42×Q8C2212yes—
255C4×#117C2212yes—
256C4×#117C2211yescharacteristic
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×#125C2312yes—
263C2×#125C2312yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×C22⋊Q8C2314yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C4×Q8Q8116yescomplemented
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2312yes—
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×#117C2312yes—
284C2×#117C2314yes—
285C2×#117C2312yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2312yes—
289C22×C4⋊C4C2314yes—
290C22×C4⋊C4C2312yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2311yescharacteristic
293C22×C42C2312yes—
294C22×C42C2312yes—
295C22×C42C2311yescharacteristic
296C22×C42C2312yes—
297#400C2314yes—
298#400C2314yes—
299#400C2314yes—
300#400C2312yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2312yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2312yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2312yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2312yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2312yes—
396#395C2314yes—
397#395C2312yes—
398#395C2312yes—
399#395C2314yes—
400#395C2314yes—
401#391C2312yes—
402#391C2312yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2314yes—
407#391C2312yes—
408#391C2314yes—
409#391C2314yes—
410#391C2312yes—
411#391C2312yes—
412#391C2314yes—
413#391C2314yes—
414#391C2314yes—
415#391C2314yes—
416#391C2314yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2312yes—
510#387C2312yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2312yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2312yes—
560#387C2312yes—
561#387C2312yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#385C2312yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2312yes—
580#385C2312yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2312yes—
585#384C2312yes—
586#384C2312yes—
587#384C2314yes—
588#384C2314yes—
589#384C2314yes—
590#384C2312yes—
591#384C2314yes—
592#383C2312yes—
593#383C2312yes—
594#383C2314yes—
595#383C2311yescharacteristic
596#383C2311yescharacteristic
597#383C2314yes—
598#383C2312yes—
599#383C2312yes—
600#383C2312yes—
601#383C2312yes—
602#383C2314yes—
603#383C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2312yes—
608#382C2314yes—
609#382C2314yes—
610#382C2312yes—
611#382C2312yes—
612#382C2314yes—
613#382C2312yes—
614#382C2314yes—
615#382C2312yes—
616#382C2314yes—
617#382C2312yes—
618#382C2312yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#382C2314yes—
623#382C2312yes—
624#381C2312yes—
625#381C2312yes—
626#381C2314yes—
627#381C2312yes—
628#381C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2311yescharacteristic
632#380C2312yes—
633#380C2314yes—
634#380C2314yes—
635#380C2314yes—
636#380C2312yes—
637#380C2314yes—
638#380C2312yes—
639#380C2311yescharacteristic
640#380C2311yescharacteristic
641#380C2312yes—
642#380C2311yescharacteristic
643#380C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2311yescharacteristic
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C22⋊C4C2311yescharacteristic
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2311yescharacteristic
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2311yescharacteristic
690#376C2312yes—
691#376C2311yescharacteristic
692#376C2312yes—
693#376C2311yescharacteristic
694#376C2311yescharacteristic
695#376C2311yescharacteristic
696#376C2311yescharacteristic
697#376C2311yescharacteristic
698#376C2312yes—
699#376C2312yes—
700#376C2314yes—
701#376C2314yes—
702#376C2312yes—
703#376C2312yes—
704C2×#95C2311yescharacteristic
705C2×#95C2312yes—
706C2×#95C2314yes—
707C2×#95C2311yescharacteristic
708C2×#95C2314yes—
709C2×#95C2312yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2314yes—
713C22×Q8—44no—
714C22×Q8C2×Q818yes—
715C22×Q8C2411yescharacteristic
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2414yes—
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C23×C4C2412yes—
723C23×C4C2411yescharacteristic
724C23×C4C2411yescharacteristic
725C23×C4C2414yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2411yescharacteristic
730C4⋊Q8—44no—
731C4⋊Q8—44no—
732#125—44no—
733#125—44no—
734#125—44no—
735#125—44no—
736C22⋊Q8—44no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739C22⋊Q8—44no—
740C4×Q8—44no—
741C4×Q8—44no—
742C4×Q8—44no—
743C4×Q8—44no—
744C4×Q8—44no—
745C4×Q8—44no—
746C4×Q8C2×Q818yes—
747C4×Q8C2×Q818yes—
748C4×Q8C2×Q818yes—
749C4×Q8C2×Q818yes—
750C4×Q8C2×Q8116yes—
751C4×Q8C2×Q8116yes—
752#117—42no—
753#117—44no—
754#117—44no—
755#117—42no—
756#117—48no—
757#117—44no—
758C2×C4⋊C4—44no—
759C2×C4⋊C4—48no—
760C2×C4⋊C4C2×Q818yes—
761C2×C4⋊C4C2×Q8116yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C22⋊C4C2411yescharacteristic
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2411yescharacteristic
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2411yescharacteristic
846C2×C22⋊C4C2412yes—
847C2×C42—44no—
848C2×C42—44no—
849C2×C42C2×Q818yes—
850C2×C42C2×Q8116yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2412yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2412yes—
858C2×C42C2412yes—
859C2×C42C2414yes—
860C2×C42C2414yes—
861C2×C42C2412yes—
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2414yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2412yes—
879C2×C42C2411yescharacteristic
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2412yes—
885#95C2412yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2412yes—
889#95C2411yescharacteristic
890#95C2411yescharacteristic
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2412yes—
897#95C2412yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2412yes—
911#95C2411yescharacteristic
912#95C2411yescharacteristic
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2411yescharacteristic
920#95C2412yes—
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2414yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980C24C2511yescharacteristic
981C2×Q8—24no—
982C2×Q8—24no—
983C2×Q8—44no—
984C2×Q8—42no—
985C2×Q8—42no—
986C2×Q8—42no—
987C2×Q8—42no—
988C2×Q8—42no—
989C2×Q8—42no—
990C2×Q8—44no—
991C2×Q8—44no—
992C2×Q8—44no—
993C2×Q8—44no—
994C2×Q8—44no—
995C2×Q8—44no—
996C2×Q8—416no—
997C2×Q8C22×Q814yes—
998C2×Q8C22×Q814yes—
999C2×Q8C22×Q818yes—
1000C22×C4—22no—
1001C22×C4—24no—
1002C22×C4—22no—
1003C22×C4—24no—
1004C22×C4—24no—
1005C22×C4—28no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—42no—
1009C22×C4—44no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4C22×Q818yes—
1017C22×C4C22×Q814yes—
1018C22×C4C22×Q814yes—
1019C22×C4C22×Q814yes—
1020C22×C4C22×Q818yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2511yescharacteristic
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2511yescharacteristic
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—44no—
1062C4⋊C4—42no—
1063C4⋊C4—44no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4C22×Q818yes—
1119C4⋊C4C22×Q818yes—
1120C4⋊C4C22×Q818yes—
1121C4⋊C4C22×Q818yes—
1122C4⋊C4C22×Q818yes—
1123C4⋊C4C22×Q814yes—
1124C4⋊C4C22×Q814yes—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—22no—
1130C22⋊C4—24no—
1131C22⋊C4—22no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C42—24no—
1135C42—24no—
1136C42—24no—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—44no—
1141C42—42no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42—44no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—42no—
1152C42—44no—
1153C42—44no—
1154C42—44no—
1155C42—44no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42C22×Q818yes—
1161C42C22×Q814yes—
1162C42C22×Q818yes—
1163C42C22×Q814yes—
1164C42C22×Q818yes—
1165C42C22×Q818yes—
1166C42C22×Q814yes—
1167C42C22×Q814yes—
1168C23—22no—
1169C23—22no—
1170C23C23×Q812yes—
1171C23#58512yes—
1172C23#58512yes—
1173C23C2611yescharacteristic
1174Q8—28no—
1175Q8—28no—
1176Q8—48no—
1177Q8—84no—
1178Q8—84no—
1179Q8—164no—
1180Q8—164no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—28no—
1195C2×C4—216no—
1196C2×C4—28no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—24no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—44no—
1252C2×C4—48no—
1253C2×C4—84no—
1254C2×C4—88no—
1255C2×C4—84no—
1256C2×C4C23×Q812yes—
1257C2×C4C23×Q812yes—
1258C2×C4C23×Q812yes—
1259C2×C4C23×Q814yes—
1260C2×C4C23×Q812yes—
1261C2×C4C23×Q814yes—
1262C2×C4C23×Q812yes—
1263C2×C4C23×Q814yes—
1264C2×C4C23×Q814yes—
1265C2×C4C23×Q812yes—
1266C2×C4#58514yes—
1267C22—22no—
1268C22—22no—
1269C22—24no—
1270C22—24no—
1271C22#350414yes—
1272C22C24×Q811yescharacteristic
1273C22C2×#58511yescharacteristic
1274C22C2×#58511yescharacteristic
1275C22C2×#58512yes—
1276C222−1+612yes—
1277C4—22no—
1278C4—22no—
1279C4—24no—
1280C4—24no—
1281C4—22no—
1282C4—22no—
1283C4—22no—
1284C4—24no—
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—42no—
1290C4—44no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4#345814yes—
1305C2—24no—
1306C2C2×#345811yescharacteristic
1307C2C2×#350411yescharacteristic
1308C2#6284911yescharacteristic
1309C2#6294012yes—
1310C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC24C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #42826C2semidirect
2. #42824C2semidirect
3. #42821C2semidirect
4. #42819C2semidirect
5. #42185C2semidirect
6. #42183C2semidirect
15. #37197C2semidirect
16. #37197C2semidirect
17. #35643C2semidirect
18. #35642C2semidirect
22. #35221C2semidirect
23. #35221C2semidirect
270. C2×C4×Q8Q8semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#428262
#428242
#428212
#428192
#421852
#421832
#397522
#394962
#391792
#389632
#381032
#378772
#376092
#375622
#371972
#356432
#356422
#353392
#353042
#352352
#352212
#351462
#349482
#348782
#341962
#341282
C2×#23202